Let be a commutative ring with 1 and be left unitary . In this papers we introduced and studied concept P-small compressible (An is said to be P-small compressible if can be embedded in every of it is nonzero P-small submodule of . Equivalently, is P-small compressible if there exists a monomorphism , , is said to be P-small retractable if , for every non-zero P-small submodule of . Equivalently, is P-small retractable if there exists a homomorphism whenever as a generalization of compressible and retractable respectively and give some of their advantages characterizations and examples.
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                                        Publication Date
                                    
                                    
                                        Thu Jul 20 2023
                                    
                                
                                        Journal Name
                                    
                                    
                                        Ibn Al-haitham Journal For Pure And Applied Sciences
                                    
                                
                                        Volume
                                    
                                    
                                        36
                                    
                                
                                        Issue Number
                                    
                                    
                                        3
                                    
                                
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                        P-small Compressible Modules and P-small Retractable Modules
                    
                                        
                    
                    
                            
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